Custom Alphas in GIMP
To add Alpha to GIMP layer


Right click on a layer in GIMP and select "Add Layer Mask..."
You will see a second thumbnail appear on the layer. Select the thumb.
Paint over your image where you want Alpha in Black and White.
When it is transparent you will see a checkered background in GIMP. 


Note on Blender
There are a few ways alpha can be implemented, I am just sharing the simplest IMO. Implementing an image that has an alpha channel built in will depend on what render engine you are using. In Cycles you will need to use a Transparency node in addition to whatever node setup you are using to utilize Alpha. BI will need several settings changed to setup alpha (A couple in the texture properties and enabled transparency in the material if memory serves me, been many years since I last used BI). EEVEE, not officially released as of time of writing doesn't seem to be working correctly using latest build on my system so will have to update later if you need to know about that one.

Edit: 
It should be mentioned, You do not have to use GIMP for painting in Blender (But it can be a nice addition afterwards for more advanced editing), you can make your texture file in Blender and then go to paint mode on your object. Blender does have some performance limitations doing this at high resolution. 


To create a new texture file for painting go to your UV image editor and click "New", then type in your file name, resolution and make sure "Alpha" is checked.
Once thats done apply your new image to your material so it is seen in the viewport on the model you want to paint
Go to texture paint mode and have fun
Always remember to save your texture file outside Blender or it will be deleted!